Suppose Kenji and Lucia are playing a game in which both must simultaneously cho

Question

Suppose Kenji and Lucia are playing a game in which both must simultaneously choose the action Left or Right. The payoff matrix that follows shows the payoff each person will earn as a function of both of their choices. For example, the lower-right cell shows that if Kenji chooses Right and Lucia chooses Right, Kenji will receive a payoff of 3 and Lucia will receive a payoff of 6.

The only dominant strategy in this game is for? ? to choose ? ?.

The outcome reflecting the unique Nash equilibrium in this game is as follows: Kenji chooses ? ? and Lucia chooses ? ?.

Explanation / Answer

Dominant strategy is a strategy for a player i.e. best response to all strategy profile of other player.

Kenji has the dominant strategy of choosing Left because it gives higher payoff to Kenji irrespective of decision of Lucia.

Nash equilibrium is a strategy profile such that for each player given strategy, it is best response. Nash equilibrium is a set of strategies such that each player is doing their best given the strategy of other player.

If Kenji chooses Left then best response of Lucia is to choose Left because payoff of 6 is better than 5.

If Lucia chooses Left then best response of Kenji is to choose Left.

Therefore, (Left; Left) is the Nash Equilibrium.

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